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<p>The class template <code>std::ratio</code> and associated templates provide compile-time rational arithmetic support. Each instantiation of this template exactly represents any finite rational number.
</p>
<h3>
<span class="editsection">[<a href="http%3A//en.cppreference.com/mwiki/index.php" title="Edit section: Compile-time fractions">edit</a>]</span> <span class="mw-headline" id="Compile-time_fractions">Compile-time fractions</span>
</h3>
<table class="t-dsc-begin">

<tr class="t-dsc-header">
<td colspan="2"> <div>Defined in header <code>&lt;ratio&gt;</code> </div>
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="ratio/ratio.html" title="cpp/numeric/ratio/ratio"> <span class="t-lines"><span>ratio</span></span></a></div></div>
</td>
<td>   represents exact rational fraction <br> <span class="t-mark">(class template)</span>
</td>
</tr>

</table>
<p>Several convenience typedefs that correspond to the SI ratios are provided by the standard library:
</p>
<table class="t-dsc-begin">

<tr class="t-dsc-header">
<td colspan="2"> <div>Defined in header <code>&lt;ratio&gt;</code> </div>
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc-hitem">
<td>  Type
</td>
<td>  Definition
</td>
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<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>yocto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000000000</span><span class="sy1">&gt;</span></span></span>, if <span class="t-lc"><a href="../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> can represent the denominator
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>zepto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000000</span><span class="sy1">&gt;</span></span></span>, if <span class="t-lc"><a href="../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> can represent the denominator
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>atto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>femto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>pico</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>nano</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>micro</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>milli</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>centi</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">100</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>deci</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">10</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>deca</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">10</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>hecto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">100</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>kilo</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>mega</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>giga</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>tera</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>peta</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>exa</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>zetta</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>, if <span class="t-lc"><a href="../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> can represent the numerator
</td>
</tr>


<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <code>yotta</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="ratio/ratio.html"><span class="kw1231">std::<span class="me2">ratio</span></span></a><span class="sy1">&lt;</span><span class="nu0">1000000000000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>, if <span class="t-lc"><a href="../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> can represent the numerator
</td>
</tr>

</table>
<h3>
<span class="editsection">[<a href="http%3A//en.cppreference.com/mwiki/index.php" title="Edit section: Compile-time rational arithmetic">edit</a>]</span> <span class="mw-headline" id="Compile-time_rational_arithmetic">Compile-time rational arithmetic</span>
</h3>
<p>Several class templates, that perform arithmetic operations on <code>ratio</code> objects at compile-time are provided.
</p>
<table class="t-dsc-begin">

<tr class="t-dsc-header">
<td colspan="2"> <div>Defined in header <code>&lt;ratio&gt;</code> </div>
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_add.html" title="cpp/numeric/ratio/ratio add"> <span class="t-lines"><span>ratio_add</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   adds two <code>ratio</code> objects at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_subtract.html" title="cpp/numeric/ratio/ratio subtract"> <span class="t-lines"><span>ratio_subtract</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   subtracts two <code>ratio</code> objects at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_multiply.html" title="cpp/numeric/ratio/ratio multiply"> <span class="t-lines"><span>ratio_multiply</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   multiplies two <code>ratio</code> objects at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_divide.html" title="cpp/numeric/ratio/ratio divide"> <span class="t-lines"><span>ratio_divide</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   divides two <code>ratio</code> objects at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>
</table>
<h3>
<span class="editsection">[<a href="http%3A//en.cppreference.com/mwiki/index.php" title="Edit section: Compile-time rational comparison">edit</a>]</span> <span class="mw-headline" id="Compile-time_rational_comparison">Compile-time rational comparison</span>
</h3>
<p>Several class templates, that perform comparison operations on <code>ratio</code> objects at compile-time are provided.
</p>
<table class="t-dsc-begin">

<tr class="t-dsc-header">
<td colspan="2"> <div>Defined in header <code>&lt;ratio&gt;</code> </div>
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_equal.html" title="cpp/numeric/ratio/ratio equal"> <span class="t-lines"><span>ratio_equal</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   compares two <code>ratio</code> objects for equality at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_not_equal.html" title="cpp/numeric/ratio/ratio not equal"> <span class="t-lines"><span>ratio_not_equal</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   compares two <code>ratio</code> objects for inequality at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_less.html" title="cpp/numeric/ratio/ratio less"> <span class="t-lines"><span>ratio_less</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   compares two <code>ratio</code> objects for <i>less than</i> at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_less_equal.html" title="cpp/numeric/ratio/ratio less equal"> <span class="t-lines"><span>ratio_less_equal</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   compares two <code>ratio</code> objects for <i>less than or equal to</i> at compile-time <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_greater.html" title="cpp/numeric/ratio/ratio greater"> <span class="t-lines"><span>ratio_greater</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   compares two <code>ratio</code> objects for <i>greater than</i> at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>

<tr class="t-dsc-sep">
<td colspan="2">
</td>
</tr>
<tr class="t-dsc">
<td>  <div class="t-dsc-member-div">
<div><a href="ratio/ratio_greater_equal.html" title="cpp/numeric/ratio/ratio greater equal"> <span class="t-lines"><span>ratio_greater_equal</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>   compares two <code>ratio</code> objects for <i>greater than or equal to</i> at compile-time  <br> <span class="t-mark">(class template)</span> 
</td>
</tr>
</table>

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